Before we present our theory we summarize some of the relevant experimental
observations and their puzzling implications that motivated our proposal.
Excluding accidental degeneracies, homogeneous TRSB at \(T_{c}\)  may only occur for a superconducting
order parameter that has at least two components, i.e., transforms
according to a two- or higher-dimensional irreducible representation
of the symmetry group [1]}. For \(\mathrm {Sr}_{2}\mathrm {Ru}\mathrm {O}_{4}\) , with \(D_{4h}\)  point group,
this leaves only two options: \(E_{u}\)  triplet
pairing that transforms like \(p_{x} \pm ip_{y}\)  or the \(E_{g}\)  singlet
pairing of the type \(d_{xz} \pm id_{yz}\) . The most recent NMR measurements
strongly favor singlet pairing [2]}, [3]}, [4]}. Furthermore,
\(\mu \) SR experiments under uniaxial stress report a clear
splitting between the superconducting transition temperature \(T_{c}\)  and the onset
temperature for broken time-reversal symmetry, \(T_{{\scriptscriptstyle \mathrm {TRSB}}} \!<\! T_{c}\)  [5]}.
For such a two-component order parameter, uniaxial stress should indeed lift the degeneracy.
In this picture, the strain-favored component first
condenses to a single-component state at \(T_{c}\) , while the strain-disfavored
component mixes-in with relative phase \(\pm \pi /2\)  at \(T_{{\scriptscriptstyle \mathrm {TRSB}}}\) .
Numerous theories for \(\mathrm {Sr}_{2}\mathrm {Ru}\mathrm {O}_{4}\)  consider either
\(p_{x} \pm ip_{y}\)  triplet pairing [6]}, [7]}, [8]}, [9]}, [10]}, [11]}
or, given the recent NMR results of Refs. [2]}, [3]}, [4]},
\(d_{xz} \pm id_{yz}\)  singlet pairing [15]}, [16]}, [17]}.
